When the blackboard presentation doesn’t work, how can we reach students with special needs? The techniques that my colleagues and I have been using are:
- use a good discovery method curriculum and provide just in time answers when my students get stuck (Just in Time Delivery)
- provide insight (Visual Models)
- come back to the same ideas and techniques in many different guises – mathematical logic may be deductive, but my students appear to develop insight from inductive logic (figure out a pattern after Many, Many Examples, perceptual learning) .
- use graphing software (Algebra as an Experimental Science, Visual Models, Many Many Examples in one small package)
- use videos so the students can rewind
- include worked out examples for the students to look at.
This post discusses just-in-time delivery. The other techniques will be discussed in subsequent blog posts.
Just in Time Delivery
Early in my teaching career, I worked at a school that was using the Carnegie Learning algebra 1 curriculum (before common core). When I first looked at the algebra 1 text, I was blown away by the content. The text started with simple questions: If you make $8 an hour and you work for 2 hours, how much will you earn? For 3 hours? For 10 hours? The questions made sense to students with a knowledge of arithmetic, but the text eventually snuck in tables, equations, and graphs as different ways of looking at the same problem. The questions were broken into tiny parts that my students could often (but not always) answer. Many of my students, unable to follow an explanation at the board, were able to progress by working through the examples. If I was able to supply answers just as they were needed, my students, who would have been lost with blackboard explanations, were able to continue work. Better yet, the breakdown of questions into tiny parts allowed me to figure out the exact point at which my students got confused.
I have successfully taught algebra to many students with learning disabilities by giving them Carnegie Learning texts and coming over to supply help just as they need it. If you have students who can work together and help each other out, the approach is probably even more effective. I have been at a number of AMTNJ meetings where the speakers mentioned supplying information just as students need it as an effective way to help the students learn. For students in grades 1-6 or students who need to relearn topics from grades 1-6 math, I really like the JUMP math common core textbooks. You can see sample grade level materials by going to the JUMP math website.
In addition, for those of you who have read Make It Stick (the science of teaching to help students remember), the authors claim that students will remember mathematics better if the students attempt to figure the material out before they get help. A discovery method curriculum with just-in-time help allows the students some time to try to figure it out on their own before before you supply the help.
I live in mortal fear that Carnegie Learning will stop publishing their original textbooks. Although they told me that they plan to stop, there are clearly other fans at other schools that are still ordering the original (pre common core) books because those original books are still being printed. The original text incorporates what is now 8th grade math (which I need to teach to many of my algebra 1 students before I can actually teach algebra 1), and progresses to include the content of a regular common core algebra 1.
If you have a good discovery method program that you are using, please share the information with the rest of us. There are probably many programs that support just in time delivery to students who are struggling. If you have another way of doing just-in-time delivery to students who cannot follow presentations made at the blackboard, please share that with us as well. Sample lessons are also welcome.
Are there other techniques that work for you when students cannot understand from blackboard presentations?
I will discuss visual models, many-many examples, and algebra as an experimental science in subsequent blog posts.